I actually found out how to get the outbound emails working on Godaddy without having to modify the php.ini file. You set the the outbound email to Godaddy's relay server which is:
relay-hosting.secureserver.net
Port 25
No Authentication
This allows new ticket emails to go out without a problem.
I did a bunch of research regarding getting the Imap email stuff working. I read some things that say Godaddy does not allow you to modify your php,ini or php5.ini file, but readother articles that said if you are on a shared Linux host that you can put your own .ini files in your directory that over ride the default ones. So I'm not sure which one to believe.
I didn't bother trying this since I wasn't interested in enabling this feature. I only want people to go to the site to create a ticket.
Thanks for the help. Good luck to all.